Question: Express your answer as a mixed number simplified to lowest terms. $19\dfrac{5}{17}-11\dfrac{2}{3} = {?}$
Solution: Find a common denominator for the fractions: $= {19\dfrac{15}{51}}-{11\dfrac{34}{51}}$ Convert ${19\dfrac{15}{51}}$ to ${18 + \dfrac{51}{51} + \dfrac{15}{51}}$ So the problem becomes: ${18\dfrac{66}{51}}-{11\dfrac{34}{51}}$ Separate the whole numbers from the fractional parts: $= {18} + {\dfrac{66}{51}} - {11} - {\dfrac{34}{51}}$ Bring the whole numbers together and the fractions together: $= {18} - {11} + {\dfrac{66}{51}} - {\dfrac{34}{51}}$ Subtract the whole numbers: $=7 + {\dfrac{66}{51}} - {\dfrac{34}{51}}$ Subtract the fractions: $= 7+\dfrac{32}{51}$ Combine the whole and fractional parts into a mixed number: $= 7\dfrac{32}{51}$